Magic-angle bilayer phononic graphene

Thanks to the recent discovery of the magic-angle bilayer graphene, twistronics is quickly becoming a burgeoning field in condensed matter physics. This Rapid Communication expands the realm of twistronics to acoustics by introducing twisted bilayer phononic graphene, which remarkably also harbors the magic angle, evidenced by the associated ultraflat bands. Beyond mimicking quantum-mechanical behaviors of twisted bilayer graphene, we show that their acoustic counterpart offers a considerably more straightforward and robust way to alter the interlayer hopping strength, enabling us to unlock magic angles (>3 degrees) inaccessible in classical twisted bilayer graphene. This study not only establishes the acoustical analog of twisted (magic-angle) bilayer graphene, providing a test bed more easily accessible to probe the interaction and misalignment between stacked two-dimensional materials, but also points out the direction to a new phononic crystal design paradigm that could benefit applications such as enhanced acoustic emission and sensing.